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GENERAL  ARTICLE
Quantum Interference of Molecules
Probing the Wave Nature of Matter
Anu Venugopalan
Anu Venugopalan is on the
faculty of the School of
Basic and Applied
Sciences, GGS
Indraprastha University,
Delhi. Her primary
research interests are in
the areas of Foundations of
Quantum mechanics,
Quantum Optics and
Quantum Information.
The double-slit interference experiment has been
famously described by Richard Feynman as containing the \only mystery of quantum mechanics". While the double-slit experiment for light
is easily understood in terms of its wave nature,
the very same experiment for particles like the
electron is somewhat more di±cult to comprehend. It has taken almost six decades after the
establishment of its wave nature to carry out
a `double-slit interference' experiment for electrons. This has set the stage for interference
experiments with atoms and molecules. In the
last decade there has been a spectacular progress
in matter{wave intereference experiments. Today, molecules with over a hundred atoms can
be made to interfere. In this article we discuss
some of these exciting developments which probe
new regimes of Nature, bringing us closer to the
heart of quantum mechanics and its hidden mysteries.
1. Introduction: The Dual Nature of Radiation
and Matter and the Birth of Quantum Mechanics
Keywords
Matter waves, wave-particle duality, electron interference,
decoherence.
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At the turn of the last century, there were several experimental observations which could not be explained
in terms of the established laws of classical physics and
called for a radically di®erent way of thinking. This
led to the development of quantum mechanics, which
is today regarded as the fundamental theory of Nature
and the most elegant tool for describing the physics
of the microworld. Some key events and developments
that set the stage for the coming of quantum mechan-
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GENERAL  ARTICLE
ics were associated with the black-body radiation spectrum (Planck, 1901), the photoelectric e®ect (Einstein,
1905), the model of the atom (Rutherford, 1911), atomic
spectra (Bohr, 1913), scattering of photons o® electrons
(Compton, 1922), the exclusion principle (Pauli, 1922),
the hypothesis of matter waves (de Broglie, 1925) and
the experimental con¯rmation of the existence of matter
waves (Davisson and Germer, 1927).
The birth of quantum mechanics is intimately linked
with discoveries relating to the nature of light. Theories
relating to the nature of light have a long and chequered
history. Is light a wave or is it made up of particles? The
earliest theory on the nature of light goes back to the
corpuscular theory of Newton in 1704. Though Christian Huygens had proposed the wave theory of light in
1690, Newton's corpuscular theory, according to which
light is composed of tiny particles or corpuscles, was the
favoured one for over a hundred years { a consequence of
Newton's towering presence and authority in the scienti¯c community at that time. In 1801, Thomas Young
performed an experiment with light where a beam of
light was passed through two parallel slits in an opaque
screen and formed a pattern of alternating light and dark
bands on a screen beyond { this we know as interference
{ a phenomenon which is associated with waves. Later,
other important experiments on di®raction and interference of light were also done, notably by Fresnel (1814)
and others that could only be interpreted in terms of the
wave theory for light. In the face of such irrefutable experimental evidence, the wave theory became the dominant and accepted theory of the nature of light in the
19th century. In 1864, James Clerk Maxwell showed
that electric and magnetic ¯elds propagated together
and that the speed of these electromagnetic waves was
identical to the speed of light. It became clear at that
point that light is a form of electromagnetic radiation.
Maxwell's theory was con¯rmed experimentally with the
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The birth of
quantum
mechanics is
intimately linked
with discoveries
relating to the
nature of light.
The wave theory
became the
dominant and
accepted theory of
the nature of light
in the 19th century.
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GENERAL  ARTICLE
The discovery of the
photoelectric effect
and its explanation
by Einstein firmly
established that light
(radiation) has a dual
nature.
In 1927, Clinton
Davisson and Lester
Germer observed the
diffraction of electron
beams from a nickel
crystal –
demonstrating the
wave-like properties
of particles for the
first time
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discovery of radio waves by Heinrich Hertz in 1886. An
experiment performed by Taylor in 1909 showed that
even the weakest light source { equivalent to \a candle
burning at a distance slightly exceeding a mile" { could
lead to interference fringes. This led to Dirac's famous
statement that \each photon then interferes only with
itself ". However, the wave nature of light was not the
¯nal word in this debate; there was experimental evidence, the photoelectric e®ect, which clearly needed an
alternate interpretation. The discovery of the photoelectric e®ect and its explanation by Einstein ¯rmly established that light (radiation) has a dual nature. In 1924,
Louis de Broglie put forth the hypothesis that matter
has a wave nature and the now famous de Broglie relation connects the wavelength ¸ of a particle with its
momentum p:
h
¸= ;
(1)
p
h being Planck's constant. While this wavelength would
be extremely small for large objects, particles like electrons have a wavelength which could be large enough to
give observable e®ects. In 1927, Clinton Davisson and
Lester Germer observed the di®raction of electron beams
from a nickel crystal { demonstrating the wave-like properties of particles for the ¯rst time { and George (G P)
Thompson did the same with thin ¯lms of celluloid and
other materials shortly afterwards. Davisson and Thomson shared the 1937 Nobel Prize for \discovery of the interference phenomena arising when crystals are exposed
to electronic beams". Their work was a landmark result
in the development of quantum theory as it provided
the critical con¯rmation of Louis de Broglie's hypothesis. Now that the wave nature of electrons was established, it remained to be seen if they indeed showed the
classic signature of the quantum world { the double-slit
interference e®ect, which would be the most satisfying
con¯rmation of the dual nature of electrons as predicted
by quantum theory.
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Most students of physics are familar with Richard Feynman's famous description of the double-slit experiment
(Figure 1) which captures the dual nature of matter
as described by quantum mechanics. Feynman goes to
great lengths to explain the apparently paradoxical phenomenon by using the example of `bullets' and `single
electrons'. The most ba²ing conclusion of this experiment is that even when there is only one electron (or
photon) ¯red at the double slit, there will be an interference pattern on the screen { something that can only be
understood by the quantum mechanical description in
terms of wavefunctions, linear superposition and probability amplitudes. In the quantum mechanical description the wave and particle aspects are inseparable and
it is as though the electron went through both slits simultaneously and the amplitudes for these combined at
the screen to give the interference pattern. Here lies the
great 'mystery' of quantum mechanics, its predictions
being completely in contrast to our cherished classical
'common-sense' perceptions.
While most people have heard about Young's doubleslit experiment for light, not many know about the experiments for electrons. Who actually performed the
double-slit interference experiment for single electrons
and when? The earliest experiment can be attributed
to Ladislaus Laszlo Marton of the US National Bureau of
Standards (now NIST) in Washington, DC, who demonstrated electron interference in the early 1950s. However, his experiment was in a Mach{Zehnder rather than
a double-slit geometry. A few years later Gottfried MÄollenstedt and Heinrich DÄ
ukertheory of the University of
TÄ
ubingen in Germany used an electron biprism to split
an electron beam into two components and observe interference between them. In 1961 Claus JÄonsson performed an actual double-slit experiment with electrons
for the ¯rst time. Finally, in 1989, the now famous
experiment involving single electrons was performed by
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Figure 1. The double-slit
interference experiment.
In the quantum
mechanical
description the
wave and particle
aspects are
inseparable.
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GENERAL  ARTICLE
These are stunning
experiments with the
largest objects ever
to show quantum
interference —
probing a hitherto
inaccesible regime
which lies in the
twilight zone
between the
classical and
quantum worlds.
Akira Tonomura and co-workers at Hitachi, Japan, where
they observed the build-up of the fringe pattern with a
very weak electron source and an electron biprism. For
details on the history of these interference experiments
with electrons the interested reader is referred to an informative article in Physics World listed at the end of
this article. In the following we will brie°y review the
Davisson and Germer experiment and discuss the classic double-slit experiment for a single electron performed
by Tonomura et al. We will then discuss recent experiments which carry interference experiments to a completely new level { molecules with as many as 100 atoms
showing quantum interference! These are stunning experiments with the largest objects ever to show quantum interference { probing a hitherto inaccesible regime
which lies in the twilight zone between the classical and
quantum worlds. This is an an area of fundamental scienti¯c curiosity and perhaps holds the key to a myriad
possibilities of practical importance.
2. The Davisson and Germer Experiment
Davisson and Germer
showed that the
electron beam was
scattered by the
surface atoms on the
nickel crystal at the
exact angles that had
been predicted for the
diffraction of X-rays by
Bragg’s formula.
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Clinton Davisson and Lester Germer performed the conclusive experimental test of Louis de Broglie's hypothesis in 1927 at Bell Labs. For this work they shared
the Nobel Prize in 1937 with G P Thomson. Their results were published in a paper entitled `The scatterring
of electrons by a single crystal of nickel' in the journal Nature in 1927. In their paper, Davisson and Germer reported their analysis of the angular distribution of
electrons scattered from nickel. They showed that the
electron beam was scattered by the surface atoms on
the nickel crystal at the exact angles that had been predicted for the di®raction of X-rays by Bragg's formula,
with a wavelength given by the de Broglie equation (1).
This was the ¯rst time that Bragg's law was applied to
electrons. In the same year, Thomson reported his experiments in which a beam of electrons was di®racted
by a thin foil. Thomson found patterns that resembled
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GENERAL  ARTICLE
Figure 2. The Davisson and
Germer experiment.
scattered
beam
the X-ray patterns.
The Davisson and Germer experiment is very simple to
understand. Electrons strike a nickel crystal which is
cut parallel to a set of its 111 planes (see Figure 2).
The kinetic energy of these electrons is controlled by
the accelerating voltage V . Electrons are scattered in all
directions at all speeds of bombardment. The intensity
of the electrons scatterred o® the target at various angles
was analyzed. It was seen that this intensity peaked for
certain critical energies at a given scatterring angle. The
Bragg condition for maximum constructive interference
is
2d sin A = m¸; m = 1; 2; :::;
(2)
where d is the spacing between the planes as shown in
Figure 2, ¸ is the wavelength and A is the angle between
the incident beam and the plane from which scatterring
is taking place (see Figure 2). From this ¯gure it is clear
that this can be re-written in terms of the angle B as:
2d cos
B
= m¸; m = 1; 2; :::
2
and
d = a sin
B
;
2
(3)
(4)
where a is the lattice spacing in the nickel crystal. This
gives us
a sin B
¸=
:
(5)
m
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GENERAL  ARTICLE
These two
experiments were
stunning validations
of the de Broglie
hypothesis – particles
can also propagate
like waves.
For nickel, a = 0:215 nm. A peak in the electron intensity at an angle Á = 50± for m = 1 gives the electron wavelength as 0:165 nm. Davisson and Germer
found that at this angle the peak corresponds to a voltage V = 54 volts. Corresponding to this voltage, the
momentum of the electron is given by
p=
q
2me eV ;
(6)
where me is the mass of the electron and e is its charge.
The de Broglie wavelength corresponding to this momentum is
h
¸ = = 0:167 nm:
(7)
p
This was undoubtedly in excellent agreement with the
experimental results. Shortly after this experiment,
Thomson demonstrated a similar interference phenomenon with electrons. These two experiments were stunning validations of the de Broglie hypothesis and the
understanding of the physical world took a whole new
meaning { particles can also propagate like waves.
3. The Hitachi Group's Double-Slit Interference
Experiment for Electrons
While the Davisson and Germer experiment left no doubt
about the wave nature of electrons, the most appealing and satisfying testimonial of the electron's wave-like
properties would de¯nitely be the classic paradigm of
quantum mechanics { the double-slit interference experiment. As already mentioned in the introduction, the
¯rst attempts to do this go back to the late 1950s when
Gottfried MÄollenstedt and Heinrich DÄ
uker of the University of TÄ
ubingen in Germany used an electron biprism
to split an electron beam into two components and observe interference between them. Following this, Claus
JÄonsson of the University of TÄ
ubingen did the experiment. In 1974 researchers led by Pier Giorgio Merli
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did the electron interference experiment at the University of Milan. The experiment was repeated in 1989 by
Tonomura et al at Hitachi in Japan. By 1989, stunning
advances in technology, particularly in electronics, made
the Hitachi group's equipment far more sophisticated,
precise and elegant. In a paper entitled `Demonstration
of Single-Electron Buildup of an Interference Pattern'
published in the American Journal of Physics in 1989,
Akira Tonomura and colleagues at the Hitachi Advanced
Research Laboratory in Japan reported the double-slit
interference experiment with single electrons. In their
experiment they used an electron microscope equipped
with an electron biprism and a position sensitive electron counting system. In the following, we describe this
experiment brie°y.
Akira Tonomura and
colleagues at the
Hitachi Advanced
Research Laboratory
in Japan reported
the double-slit
interference
experiment with
single electrons.
Electrons are emitted one by one from the source in the
electron microscope and they encounter the biprism (see
Figure 3). These electrons were accelerated to 50,000
volts. Electrons having passed through on both sides of
the ¯lament were then detected one by one as particles
at the detector. The detectors used were so good that
even a single electron would be detected with a hundred
percent e±ciency. At the beginning of the experiment
bright spots began to appear { these were signatures of
electrons detected one by one as particles. These bright
Figure 3. Set- up for doubleslit interference with single
electrons.
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GENERAL  ARTICLE
The Hitachi group’s
experiment clearly
demonstrated that
electrons behave like
waves as described
by quantum
mechanics.
The electron biprism
invented in 1953 by
Gottfried Möllenstedt
has proven to be an
important tool in the
study of electron
waves.
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spots in the beginning appear to be randomly positioned
on the detector screen. It may be noted that only one
electron is emitted at a time. When a large number
of electrons is accumulated over time, a pattern that
looks like regular fringes begins to appear on the detector screen. After about twenty minutes very clear
interference fringes can be seen { these fringes are made
up of accumulated bright spots, each of which records
the detection of an electron! Each time a bright spot
is seen, we understand it as an electron detected as a
`particle" and yet, the build-up over time of an unmistakable inteference pattern is undoubtedly a signature
of waves! Keeping in mind that that there was only
one electron entering the set-up at a time, the Hitachi
group's experiment clearly demonstrated that electrons
behave like waves as described by quantum mechanics.
The interference pattern is a consequence of the possibilities of two di®erent paths (amplitudes) for the single
electron to pass through as it encounters the biprism
{ a situation exactly equivalent to a single electron encountering a double-slit. The out of the way chance
that the pattern is due to two electrons being together
(electron{electron interaction) is completely ruled out
in the experiment as the seond electron is not even produced from the cathode of the electron microscope till
long after the ¯rst electron is detected.
It is easy to see how the experiment implements the
double-slit situation. At the heart of the Hitachi group's
experiment was the electron biprism. The electron biprism was invented in 1953 by Gottfried MÄollenstedt. For
the past ¯ve decades it has proven to be an important
tool in the study of electron waves and applications in
solid state physics and holds tremendous potential for
applications in modern nanotechnology. Together with
his PhD student, Heinrich DÄ
uker, MÄollenstedt developed
the electron biprism. This initially consisted of a 1¹m
thin wire which was chargeable through a voltage source.
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GENERAL  ARTICLE
The biprism of the kind that was used by the Hitachi
group consists of two grounded plates with a ¯ne ¯lament between them. The ¯lament has a positive potential with respect to the plates. The ¯lament used by
the group was thinner than 1 micron in diameter. If the
incoming electron wave is given by
à = eikz z ;
(8)
the action of the biprism is to de°ect the beam. If the
electrostatic potential in the xz-plane is V (x; z), then
the de°ected wave is:
³
´
me Z z
Ã(x; z) = exp ikz z ¡ 2
V (x; z 0 )dz 0 :
(9)
h
¹ kz ¡1
In the experiment, the kinetic energy of the electrons,
h2 kz2
¹
>> ejV (x; z)j. There are two possible ways this
2m
wave can be de°ected by the biprism, depending on
which side it passes by. In each case, the de°ected wave
ikx x
can be approximated as eikz z§e
upto a constant factor, where
me Z 1 ³ @V (x; z 0 ) ´
kx = ¡ 2
dz 0 ;
x=a
@x
¹h kz ¡1
(10)
taking into account the fact that V (x; z) = V (¡x; x),
i.e., the potential is symmetrical. After de°ection, the
waves propagate towards the centre as kx > 0. This de°ection can be viewed as some sort of an impulse that
each wave would experience { having the same amplitude but di®erent signs depending on which side of the
¯lament they pass. The overlapping of these two amplitudes in the observation plane would then give rise to
the wave:
Ã(x; z) = ekz z (e¡ikx x + eikx x ):
(11)
The probability distribution corresponding to this would
contain an interference term, 4 cos2(kx x), and this is
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GENERAL  ARTICLE
The double-slit
experiment with
electrons is
transformative, being
able to convince even
the most die-hard
sceptics of the truth of
quantum mechanics.
what is observed. In the Hitachi group experiment, parameters were chosen to give a fringe spacing of the
pattern of the order of 900 º
A. The electrons were detected using a two-dimensional position sensitive electron counting system. This system comprised of a °ourescent ¯lm and a photon counting image acquisition system. (For more details on this stunning experiment, the
interested reader is referred to the literature listed at the
end of the article.) Some readers might be aware that
in September 2002, the double-slit experiment of Claus
JÄonsson was voted \the most beautiful experiment" by
readers of Physics World. To quote Robert Crease in an
article dicussing this poll, \The double-slit experiment
with electrons possesses all of the aspects of beauty.... It
is transformative, being able to convince even the most
die-hard sceptics of the truth of quantum mechanics".
Interestingly, unlike Young's double-slit experiment for
light, the double-slit interference experiment for electrons has nobody's name attached to it.
The experiment by Tonomura and colleagues at Hitachi
unambiguosly demonstrated the single electron interference phenomenon in all its glory, brilliantly capturing
the image of the interference patterns in the now famous
picture (Figure 4).
Figure 4. Single electron
events build up to from an
interference pattern in the
double-slit experiments:
The number of electrons
accumulated on the screen.
(a) 8 electrons; (b) 270 electrons; (c) 2000 electrons;
(d) is 20 min.
Reproduced from
http://www.hqrd.hitachi.co.jp/em/
doublislit.cfm, with permission
from the authors.
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4. Interference Experiments with Atoms, Molecules, Bucky Balls and More
What is the limit
Clearly, the wave nature of matter has been demonstrated beyond doubt with the experiments mentioned
and discussed in the previous sections. It is often argued
that this uniquely quantum mechanical feature escapes
our everyday perception because of the `smallness' of
Planck's constant, h being as small as 6:6 x 10¡34 Js.
For a macroscopic object this would make the de Broglie
wavelength so small that its quantum nature (waveparticle duality) would not be observable. However, this
has been no deterrent for a large number of brave experimentalists who have veri¯ed the wave nature of matter not only for electrons but also for atoms, dimers,
neutrons, molecules, noble gas clusters and even Bose{
Einstein condensates. Quantum leaps in technology and
sophisticated instrumentation have made dreams of these
gedanken experiments a reality. An interesting question
that arises is, how far can we go with larger objects?
What is the limit for observing this quantum feature
in terms of size, mass, complexity? In the following
we describe a recent set of experiments which demonstrate quantum interference in some of the most massive
molecules { C60 and C70 fullerenes and tetraphenylporphyrin molecules which are biological molecules present
in chlorophyll and haemoglobin and are twice the size of
fullerenes. These experiments could hold the key to answering fundamental questions about quantum mechanics and the nature of the quantum{classical transition
and more.
quantum feature in
for observing this
terms of size,
mass, complexity?
Figure 5. The C-60 fullerene molecule.
Picture downloaded from http://
commons.wikimedia.org/wiki/
Image:Fullerene-C60.png.
C60, the third allotropic form of carbon was discovered
in 1985 by Kroto and colleagues. These carbon molecules have a structure of a truncated icosahedron (see
Figure 5). The truncated icosahedron has 12 pentagon
and 20 hexagon rings and has 60 vertices { the shape of
a soccer ball. These molecules have been called `buckminsterfullerenes' or just 'fullerenes' because of their
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GENERAL  ARTICLE
This is a fascinating
result – intuitively
one would expect a
60 atom molecule
like the fullerene to
behave more like a
classical particle
than like a quantum
mechanical particle!
striking resemblance to geodesic structures ¯rst discussed
by Leanardo da Vinci and then implemented in architecture by the architect Buckminster Fuller. In a paper
published in Nature in 1999, the group led by Anton
Zeilinger in Vienna observed de Broglie wave interference of the buckminsterfullerene C60 { the most stable
fullerene with a mass of 720 atomic units, composed of
60 tightly bound carbon atoms. This is a fascinating result { intuitively one would expect a 60 atom molecule
like the fullerene to behave more like a classical particle
than like a quantum mechanical particle! In the following we brie°y describe this experiment.
Fullerene molecules were brought into the gas phase by
sublimating the powder form in an oven at a temperature of approximately 900 K. Molecules are ejected one
by one through a small slit in the oven. The de Broglie
wavelength of these molecules (uniquely determined by
the momentum of the molecule) is ¸ = 2:8 pm. It turns
out that the de Broglie wave length is approximately 400
times smaller than the size of the particle! The interference pattern expected would therefore be very small
and very sophisticated machinery will be needed to see
it. The di®racting element used by the group was a
nanofabricated free standing silicon nitride grating with
a grating constant d = 100 nm and a slit opening of
approximately 50 nm. After free evolution over 1 meter, the fullerene molecules are detected via thermionic
ionization by a tightly focused Argon ion laser beam
operating at 24 W. The positive ions are counted by
a secondary electron counting system. The counts, as a
function of position clearly showed a di®raction pattern.
Note that just as in the case of the Hitachi experiment,
the pattern is built up atom by atom. The experiment
ensures that there is no interference between two or more
particles during their evolution in the apparatus { so this
is indeed a single particle quantum phenomenon.
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From C60, the group has gone on to repeat the experiment for larger, more complex molecules. Starting ¯rst
with the C70 fullerene, the group demonstrated this remarkable phenomenon in C60F48 { a °uorofullerene {
which at 1632 atomic units is the largest and most complex molecule till date to show quantum interference.
The group also demonstrated quantum interference for
tetraphenylporphyrin, a derivative of a biodye which is
found in chlorophyll. This is the ¯rst biomolecule exhibiting wave nature and has a spatial extent of 2nm {
almost twice as much as C60 . There is hardly any need
to emphasize that these large molecules are, in many respects, like classical objects. They can store a lot of internal energy in many degrees of freedom. When heated
to about 3000 K, fullerenes can emit electrons, photons
and even diatomic carbon molecules. This is similar to
a hot object glowing and emitting black-body radiation.
This makes these experiments even more remarkable as
they achieve nothing less than capturing the underlying
quantum footprints (the wave-particle duality) of large
and complex classical-like objects. This begs the question: Is there a limit to the size and complexity of the
object that can show quantum interference? This question leads us to the age-old debate about the classical{
quantum transition and the connection between these
two complelety di®erent descriptions of reality. It is often argued that quantum mechanics is the description
for an abstract micro world far removed from reality
while classical mechanics describes the physics of the
macro world of our everyday experience. But the macro
is ¯nally composed of the micro! Where then, is the
boundary, if any? These spectacular experiments o®er
the tantalizing possibility of probing the twilight zone
between quantum and classical worlds by performing
interference experiments with increasingly heavier and
complex objects.
C60F48
(a fluorofullerene )
is the largest and
most complex
molecule till date
to show quantum
interference.
These spectacular
experiments offer the
tantalizing possibility
of probing the twilight
zone between
quantum and
classical worlds by
performing
interference
experiments with
increasingly heavier
and complex objects.
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GENERAL  ARTICLE
Apart from confirming
the qualitative and
quantitative
predictions of the
decoherence theory,
these experiments
allow one to estimate
the vacuum conditions
that are required for
the successful
observation of
quantum interference
of much larger
objects.
4.1 The Quantum-Classical Boundary and Decoherence
A widely accepted explanation for the appearance of
classical like features from an underlying quantum world
is the environment induced decoherence approach. According to this theory, coupling to a large number of
degrees of freedom (the environment) results in a loss of
quantum coherence which leads to emergent classicality. In the context of the experiments described above
for fullerenes and other large molecules, an important
decoherence mechanism comes from its interaction with
particles from the background gas. By °ooding the interferometer with various gases at low pressure Anton
Zeilinger's group studied the e®ect of decoherence on
the inteference phenomenon. In fact, in keeping with
the theoretical predictions, they saw an exponential decrease of the observed fringe visibility. It is interesting
to note that such decoherence which is caused by collisions is almost impossible to test in the usual matter{
wave interferometry with smaller particles (like electrons
and neutrons) as the particles are themselves so light
that they would be kicked out of the interferometer after
colliding with a gas particle. In the case of fullerenes and
larger molecules, the molecules themselves are heavy
enough to remain in the interferometer after a typical
collision. Apart from con¯rming the qualitative and
quantitative predictions of the decoherence theory, these
experiments allow one to estimate the vacuum conditions that are required for the successful observation
of quantum interference of much larger objects. The
surprising observation by the group was that collisions
would not limit quantum interference even for an object
as large as a virus provided the background pressure of
the gas is reduced to below 3 x 10¡10 mbar.
5. Conclusions
The matter{wave interference experiments of massive
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molecules described above have allowed us to probe and
explore a new regime of Nature and opened up the possiblity of experimentally studying the elusive quantum{
classical boundary. These stunning studies have demonstrated beyond doubt that the quantum nature of large
objects can indeed be captured experimentally in the
classic paradigm of the double-slit interference and diffraction set-ups. Important decoherence mechanisms
have been studied and identi¯ed and the good news is
that it is possible to carry these experiments further for
heavier and more complex molecules. Infact, there is
talk of doing these interference experiemnts for proteins
like insulin and then on to larger proteins, clusters and
nanocrystals. In the last two decades matter{wave interferrometry have demonstrated e®ects that were previously unthinkable. More importantly, they have opened
up exciting possibilities of exploring questions of fundamental interest in the foundations of quantum mechanics { like the quantum{classical boundary. Imaginative
and novel ideas continue to fuel the ¯eld and it can be
safely said that in our pursuit of the \only mystery of
quantum mechanics" the best and the most interesting
experiments are yet to come.
These stunning
studies have
demonstrated beyond
doubt that the
quantum nature of
large objects can
indeed be captured
experimentally in the
classic paradigm of
the double-slit
interference and
diffraction set-ups.
Address for Correspondence
Anu Venugopalan
University School of Basic
and Applied Sciences
GGS Indraprastha University
Kashmere Gate
Delhi 11 0 453, India.
Email:
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Suggested Reading
The topics touched upon in this article cover several references. The interested reader may look at some of the
following:
[1]
[2]
R P Feynman et al, The Feynman Lectures, Vol.3, Addison-Wesley, 2006.
The Double-Slit Experiment, Physics World, p.15, September 2002. An extended version of this article
including three letters about the history of the double-slit experiment with single electrons is available at http:/
/physicsworld.com/cws/article/print/9745.
[3]
A Tonomura et al., Demonstration of single electron build up of an interference pattern, American Journal
of Physics, Vol.57, No.2, February 1989. A nice description of this experiment can also be found at the Hitachi
web site: http://www.hqrd.hitachi.co.jp/global/doubleslit.cfm.
[4]
A non-technical description of the Fullerene diffraction experiments can be found at the web site of Anton
Zeilinger’s Research group at the Universitit Wien, Austria: http://www.quantum.univie.ac.at/research/
matterwave/c60/index.html.
[5]
Anu Venugopalan, The Coming of a Classical World, Resonance: Journal of Science Education,Vol.9, No.10,
2004. The birth of quantum mechanics is intimately linked with discoveries relating to the nature of light.
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